Conditioning conjecture for linear time-invariant system identification

Consider the least squares optimization problem arising from linear time-invariant system identification. Its stationary points correspond to the eigenvalues of a rectangular multiparameter eigenvalue problem obtained via the first-order optimality conditions.

Conditioning conjecture. The global optima of the underlying optimization problem are among the best-conditioned eigenvalues of the rectangular multiparameter eigenvalue problem.

The conjecture is motivated by numerical experience with system identification and related globally optimal parameter-identification problems, but the source gives no proof or evidence of resolution.